Question

[trần ngọc diệp]

tính

4/5x9 + 4/9x13 + 4/13x17 + 4/ 17x21 + 4/ 21x25

Answer 1

[ﾟ°☆Morgana ☆°ﾟ ( TCNTT )]

4/5x9 + 4/9x13 + 4/13x17 + 4/ 17x21 + 4/ 21x25=27.911628241

Answer 2

[Edogawa Conan]

Ta có:

\(\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}+\frac{4}{21\times25}\)

= \(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+\frac{1}{21}-\frac{1}{25}\)

= \(\frac{1}{5}-\left(\frac{1}{9}+\frac{1}{9}\right)-\left(\frac{1}{13}-\frac{1}{13}\right)-\left(\frac{1}{17}-\frac{1}{17}\right)-\left(\frac{1}{21}-\frac{1}{21}\right)-\frac{1}{25}\)

= \(\frac{1}{5}-\frac{1}{25}\)

= \(\frac{5}{25}-\frac{1}{25}=\frac{4}{25}\)